Nonparametric Nonstationary Regressions Incontinuous Time

Abstract

This paper extends non parametric estimation to time homogeneous nonstationary diffusion processes where the drift and the diffusion coefficients are function of a multivariate exogenous time dependent variable Z. We base our estimation framework on a discrete sampling of data, following a recent stream of literature. We prove almost sure convergence and normal asymptotic distribution using the concept of multivariate occupation densities, in order to make the multivariate kernel estimation meaningful in the context of nonstationary time processes. We also provide an extension of this model when Z is a long memory process of dimension 1.